Answer: In 1–10, find a formal solution to the given

Chapter 10, Problem 10E

(choose chapter or problem)

In Problems 1-10, find a formal solution to the given initial-boundary value problem.

$\frac{\partial u}{\partial t}=3 \frac{\partial^{2} u}{\partial x^{2}}+x, \quad 0<x<\pi, \quad t>0$

$u(0, t)=u(\pi, t)=0, \quad t>0$

$u(x, 0)=\sin x, \quad 0<x<\pi$

Equation Transcription:

$\frac{\partial{}u}{\partial{}t}=3\frac{{{\partial{}}^{2}u}^{\ }}{{\partial{}x}^{2}}+x,\ \ \ 0<x<\pi{},\ \ \ \ t>0$

$u(0,t)=u(\pi{},t)=0,\ \ \ \ \ t>0$

$u(x,0)=sin\ x,\ \ \ 0<x<\pi{}$

Text Transcription:

partial u/partial t=3 partial^2 u/partial x^2+x, 0<x<pi, t>0

u(0,t)=u(pi,t)=0, t>0

u(x,0)=sin x, 0<x<pi

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